Universal Computing Machine for Number Genetics in the Proportiones Perfectus Theory

The proportiones perfectuslaw states that =is a proportione perfectusif 1≤≤such that for an arbitrary positive integerℎ, there exists an integer sequence defined simultaneously by the quasigeometric relation ℎ=ℎ,≥1and the arithmetic relationℎ=ℎ+ℎ,≥1.When ==1,_^is the golden mean. When =2,=1,is the silver mean. In previous workswe introduced the theory of number genetics –a framework of logic within which the golden section is studied. In this work we apply the concept to all proportiones perfectus.Let be defined as above. Furthermore, let ℎsatisfy =≠ℎ.Now let be with ℎ=1.Again let be defined as .A robust universal computing machine is herein developed for the purpose of establishing the relationship ℎ=±ℎ,,≥1,which relationship is key to the logic protocol. It is clear therefore that this system of logic presents as the building block of every (including itself) within a particular regime. Clearly number genetics takes central place in the proportiones perfectus theory.